Boston Housing Prices EDA in Python

I'll load the dataset and inspect it first — showing shape, columns, and basic statistics.

The Boston Housing dataset is loaded with 506 rows and 14 columns: CRIM, ZN, INDUS, CHAS, NOX, RM, AGE, DIS, RAD, TAX, PTRATIO, B, LSTAT, and MEDV (the target — median home value in 1000s USD).

Key insights from the statistics:

• CRIM (per capita crime rate) is heavily right-skewed — median is 0.26 vs. a mean of 3.61 and max of 88.98, meaning a few high-crime areas pull the average up.
• RM (average rooms per dwelling) is fairly normally distributed around a mean of ~6.28, with a range of 3.56 to 8.78.
• CHAS (Charles River dummy) is binary — only ~6.9% of tracts border the river.
• NOX (nitric oxide concentration) ranges from 0.385 to 0.871, indicating variation in air quality across tracts.
• AGE (proportion of pre-1940 units) has a median of 77.5%, showing most neighborhoods have older housing stock.
• PTRATIO (pupil-teacher ratio) ranges from 12.6 to 22.0, with a mean around 18.5.
• LSTAT (% lower status population) ranges from 1.7% to 37.97%, capturing economic disadvantage.
• MEDV (median home value, in 1000s USD) has a mean of ~22.5 (i.e., 22,500 USD at the time), with a max of 50 (50,000 USD) — the max is likely censored/capped.

The describe() output covers all the basic statistics you'd need for a first look at this dataset.

The distribution of house prices (MEDV) has been plotted successfully. The histogram shows a roughly normal distribution centered around 20,000–22,000 USD, with a slight right skew. A notable spike appears at 50,000 USD — this is a well-known artifact where values were capped/censored at 50, meaning any home valued at 50,000 USD or above was recorded as exactly 50. Excluding that cap, the bulk of homes fall in the 15,000–30,000 USD range, with a long tail of lower-priced homes below 10,000 USD.

The correlation heatmap and the sorted correlation values are already available, so the goal is fully answered.

Top features correlated with MEDV (house price):

| Feature | |Cor| | Interpretation | |---|---|---| | LSTAT | 0.74 | % lower-status population — higher poverty strongly depresses home values | | RM | 0.70 | Average rooms per dwelling — more rooms strongly increase value | | PTRATIO | 0.51 | Pupil-teacher ratio — worse school ratios associate with lower prices | | INDUS | 0.48 | Industrial land proportion — more industry nearby lowers prices | | TAX | 0.47 | Property tax rate — higher taxes track with lower values |

The two dominant features are LSTAT and RM, both with correlations above 0.7. LSTAT is negatively correlated (more lower-status residents → lower price), while RM is positively correlated (more rooms → higher price). There's a sharp drop to the third feature (PTRATIO at 0.51), suggesting these two are the strongest linear predictors of house price. The remaining features have moderate-to-weak correlations below 0.5.

The top 3 features correlated with price are LSTAT, RM, and PTRATIO. Let's create scatter plots for each against MEDV.

The scatter plots for all three top features are now displayed. Here are the key takeaways from each:

LSTAT vs MEDV (r = -0.74): Strong negative relationship with a clear curved pattern. Prices drop sharply as the lower-status population percentage increases from ~5% to ~20%, then flatten. A few outliers exist at very high LSTAT values with unusually high prices.

RM vs MEDV (r = 0.70): Strong positive, roughly linear relationship. Each additional room adds meaningfully to home value, though variance increases at higher room counts. There's a notable cluster of homes capped at the 50,000 USD maximum (MEDV = 50), which likely distorts the true relationship at the high end.

PTRATIO vs MEDV (r = -0.51): Moderate negative relationship, but the scatter is much wider. The pattern is less clean — while lower pupil-teacher ratios tend to pair with higher prices, the signal is noisy. This confirms it's a weaker predictor compared to LSTAT and RM.

One important observation across all three plots: the horizontal line of points at MEDV = 50 suggests the original dataset censored prices at 50,000 USD, which may dampen the observed correlations, especially for RM and LSTAT where high-feature-value homes are most affected.